Series Tuning

[BAM]

Hey everyone,

In this thread, I'd like to explore the effects of series tuned loudspeakers (multi-chamber vented designs). There is one type in particular that I would like to analyze, as shown in the attached image file. In it, a single chamber is vented to the next chamber, which is then vented to the outside. Does this effectively produce two tuning points?

Is there a more effective way to model multi-chamber bass reflex enclosures? Must they be analyzed as complex mass-spring systems or are there rules of thumb that can be applied?

[MJK]

I have a MathCad worksheet of exactly this enclosure design available. You end up with three impedance peaks, two tuning points, and a sharp null in the SPL plot which is probably not very audible. Fostex has enclosures like this spec'ed out for several of their full range drivers and I have analyzed a couple and they are pretty good performers. You might start by studying the Fostex designs.

There is also an article in this months audioXpress of a three port system, an extra external port in the top chamber, with some design rules of thumb and measured response and inpedance curves. I also remember seeing a couple of analyses and measurements of the Fostex designs on the web but cannot recall the site names or URLs, probably a Google search will find them again.

[BAM]

Well, I was hoping to discuss the workings of the simple system in order to use that discussion as a springboard to the analysis of more complex multi-chamber, multi-vents, such as the one in the next picture. It is like a typical dual-chamber reflex enclosure, with both of the vents exiting into a third, tuned chamber. This came out of a thought about the 8th-order bandpass configuration used by Bose in their Acoustimass modules. Vent "d" exits to the outside of the enclosure.

And now here's the question that's so difficult that nobody wants to answer it: What method could I use to analyze this system? Is there an equation which can be solved for each chamber? Doing a little math is no problem for me.

[MJK]

To solve that system with simple models you would have to derive and write out the equations of motion and then solve them. It would take some time and skill but it could be done. The simplest solution would be to treat varaious regions as lumped parameters in which case you would probably end up with one equation for each mass, a total of five if I counted right, all coupled together by spring elements. A more accurate solution would require finite element modeling.

[BAM]

Attached is a diagram of the mass-spring system embodied in the triple-chamber resonant system I just described.

Each chamber of the enclosure, when only considering the vents exiting from it, has a natural frequency, with the last chamber having a natural frequency that is chosen to be between the natural frequencies of the top two chambers, such that output from the two chambers over a range of frequencies will excite the last chamber, which is coupled to the exterior environment. It's my hypothesis that this system can be designed to provide resonant loading over a broad range of frequencies, or over a narrow range of frequencies with very high magnitudes of excursion present in the exiting port (d) and thus increased output over the resonant range. A broad plateau of resonant output could then be created by appropriately choosing the spacing of the tuning frequencies of the first two chambers. I've sketched a graph which shows this -- I'll attach it in the next post.

[BAM]

Attached is the graph that shows the way the response through the resonantly-loaded range could be shaped based on the spacing of the tuning frequencies of the two smaller chambers which exit into the third. Since the third chamber would resonantly load the two vents exiting into it, the resonance of those other two vents would quickly be overwhelmed by the resonant action of the third vent, exiting to the outside, if those vents were not already resonantly loading the driver, which continues to supply stimulus at a frequency. When the peaks are spaced closely together, the gain in output can become enormous (at the expense of transient response due to the resonant nature of the loading).

These conclusions all suppose my hypothesis in the last post is correct -- that the next chamber can be driven by the ports exiting from the previous chamber as though the next chamber were being driven by a cone driver. The next chamber also stifles the resonant motion of the mass of air in each vent that exits into the next chamber from the preceding chambers, if the tuning frequency of the previous and the next chamber(s) coincide. In the case of the design I've put forth, the third chamber behaves as an acoustic bandpass filter, increasing the order of the rolloff of resonant activity above and below the resonant region by some number. (I guess 4.)

Also, my hypothesis takes into account that at frequencies which below all tuning frequencies (Fch) of the chambers that precede the final chamber, the vents in those chambers will become completely unloaded (the characteristic of vented boxes that necesitates a rumble filter). At those frequencies below all Fch, I predict that the enclosure will behave as a single, contiguous air space, tuned by the final vent to a Fb, as in a typical vented box. So the total effective number of tuning frequencies would actually be four. The objective in box design would be to get all these tuning frequencies to line right up, one after the other.

A similar form of resonant loading is achieved in the older triple-chamber Bose Acoustimass modules, which series-tunes both the front and rear chamber of a sixth-order bandpass subwoofer with the third, larger chamber which exits to the outside. Much of what I'm saying about the way this enclosure would behave comes from what I know about the way the 8th-order bandpass enclosure behaves.

I think this merits some experimentation on my part. My October Break is in two weeks. Perhaps I'll be able to build a working enclosure of the type I've just proposed. In the mean time, I'd like to know what you think of my logic.

[BAM]

here's something -- what about electroacoustic modeling methods? Would it be possible to design a circuit whose resonant behavior would act like this triple-chamber reflex enclosure, and then analyze it using something like SPICE?

[qi]

Hi BAM

This is good stuff!

Please keep it going...

[BAM]

We really need to get F4ier in here. His Subwoofer Simulator program works from electroacoustic models of the loudspeakers it simulates. We already know what circuit elements define a port, and what circuit elements define a volume of air, and a cone driver with defined parameters, etc., so the trick is really going to be figuring out what the circuit needs to look like. He already has a model that deals with series tuning, because one of the forms of sixth-order bandpass enclosures that his program simulates uses series tuning.

I wish his Subwoofer Simulator program could use "plug-in" modules for various enclosure designs, so that people could write their own plug-ins for different electroacoustic models, and then his program would run the sim. That would be cool. But barring that, perhaps people who know how to do this type of circuit modeling could help us figure out how to develop our own circuit model. From there, I could probably find a decent PSPICE tutorial somewhere online, and I have access to PSPICE on campus. (I'm an engineering-technology student at Purdue University).

This will be one crazy enclosure type that Bose didn't invent.

[qi]

NICE!

I'm all ears...